COMAP Pathfinder -- Season 2 results II. Updated constraints on the CO(1-0) power spectrum

We present updated constraints on the cosmological 3D power spectrum of carbon monoxide CO(1-0) emission in the redshift range $2.4$-$3.4$. The constraints are derived from the two first seasons of Carbon monOxide Mapping Array Project (COMAP) Pathfinder line-intensity mapping observations aiming to trace star-formation during the Epoch of Galaxy Assembly. These results improve on the previous Early Science (ES) results through both increased data volume and improved data processing methodology. On the methodological side, we now perform cross-correlations between groups of detectors (''feed-groups''), as opposed to cross-correlations between single feeds, and this new feed-group pseudo power spectrum (FGPXS) is constructed to be more robust against systematic effects. In terms of data volume, the effective mapping speed is significantly increased due to an improved observational strategy as well as better data selection methodology. The updated spherically- and field-averaged FGPXS, $\tilde{C}(k)$, is consistent with zero, at a probability-to-exceed of around $34\,\%$, with an excess of $2.7\,\sigma$ in the most sensitive bin. Our power spectrum estimate is about an order of magnitude more sensitive in our six deepest bins across ${0.09\,\mathrm{Mpc}^{-1} < k < 0.73\,\mathrm{Mpc}^{-1}}$, as compared to the feed-feed pseudo power spectrum (FPXS) of COMAP ES. Each of these bins individually constrains the CO power spectrum to ${kP_\mathrm{CO}(k)< 2400-4900\,\mathrm{\mu K^2 Mpc^{2}}}$ at $95\,\%$ confidence. To monitor potential contamination from residual systematic effects, we analyze a set of 312 difference-map null tests and find that these are consistent with the instrumental noise prediction. In sum, these results provide the strongest direct constraints on the cosmological 3D CO(1-0) power spectrum published to date.